Labor Market Analysis
Exploratory Data Analysis
Marjorie Blanco, Joe Thomson, Haodi Tu
Data
We used data from the 2016 ACS for Puerto Rico to examine wage gaps between individuals with different education levels. Our research questions are: 1) How do earnings vary by education level? 2) How does the premium for education vary by gender? The 2016 ACS is a nationally representative sample of 5194. The household survey includes questions pertaining to each household member’s demographic characteristics and labor market activity.
We restrict our sample to these three racial groups: White, Black and Other. In addition, given our goal of examining earning differences by gender and marital status and the reporting of earnings in the ACS on an annual basis (wages, salary, commissions, bonuses, tips, and self-employment income during the past 12 months), we restrict our sample to full-time year-round (FTYR) workers. We define FTYR workers as individuals who report positive earnings over the past year, who worked at least 40 of the past 52 weeks, and who worked at least 35 hours per week in a usual work week over this period.
EDA Insights:
For our exploratory analysis we looked at population breakdowns by education, age, marital status, gender, race, earnings, and work hours. We applied filters on education (HS diploma or above), age (18-64), and work hours (>35/week).
An earnings histogram identified a default maximum amount of earnings (189k) which we also filtered out of the data. The earning distribution is progressive above the median, but drops off sharply below the median, likely indicating the presence of a minimum wage. The correlation between age and earnings is very weak (.23). Likewise, earnings is very weakly correlated with hours worked among those who work more than 35 hours per week. However, white individuals appear to have an earnings premium over other races, and both married and divorced individuals appear to have an earnings premium over those who have never been married. Given that the correlation between age and earnings was weak, this may be due to other qualitative factors possessed by those who get married. Married was recategoried to married, divorced and never married. Men also appear to earn a small premium over women.
The age distribution of full time workers is skewed towards older adults, possibly indicating that younger workers have trouble finding full-time work, wait to enter the workforce, or are leaving the territory.
Preliminary Econometric Estimates
First Model:
\(Earning = \beta_0 + Divorced * \beta_1 + NeverMarried * \beta_2 + Female * \beta_3 + RaceBlack * \beta_4 + RaceOther * \beta_5 +\)
\(SomeCollege * \beta_6 + Associate * \beta_7 + Bachelor * \beta_8 + Master * \beta_9 + Professional * \beta_10 + Doctoral * \beta_11 + Age * \beta_12\)
##
## Call:
## lm(formula = PERNP ~ Divorced + NeverMarried + Female + RaceBlack +
## RaceOther + SomeCollege + Associate + Bachelor + Master +
## Professional + Doctoral + AGEP, data = ss16ppr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43715 -9218 -2930 5352 98732
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12561.11 1109.02 11.326 < 0.0000000000000002 ***
## Divorced -1185.01 548.34 -2.161 0.030735 *
## NeverMarried -2990.72 519.43 -5.758 0.00000000902 ***
## Female -4846.95 431.25 -11.239 < 0.0000000000000002 ***
## RaceBlack -1176.12 591.26 -1.989 0.046733 *
## RaceOther -2133.58 579.76 -3.680 0.000236 ***
## SomeCollege 4232.33 694.53 6.094 0.00000000118 ***
## Associate 4151.64 688.15 6.033 0.00000000172 ***
## Bachelor 12333.05 586.55 21.027 < 0.0000000000000002 ***
## Master 17780.48 812.08 21.895 < 0.0000000000000002 ***
## Professional 28122.73 1475.26 19.063 < 0.0000000000000002 ***
## Doctoral 35651.82 1615.88 22.063 < 0.0000000000000002 ***
## AGEP 286.21 21.04 13.604 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14920 on 5181 degrees of freedom
## Multiple R-squared: 0.2465, Adjusted R-squared: 0.2448
## F-statistic: 141.3 on 12 and 5181 DF, p-value: < 0.00000000000000022## [[1]]
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## [[4]]
##
## Call:
## lm(formula = log(PERNP) ~ Divorced + NeverMarried + Female +
## RaceBlack + RaceOther + SomeCollege + Associate + Bachelor +
## Master + Professional + Doctoral + AGEP, data = ss16ppr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.56257 -0.30721 -0.03127 0.27682 1.69744
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.5837348 0.0331079 289.470 < 0.0000000000000002 ***
## Divorced -0.0401003 0.0163699 -2.450 0.014333 *
## NeverMarried -0.1035958 0.0155069 -6.681 0.0000000000262869 ***
## Female -0.1377478 0.0128744 -10.699 < 0.0000000000000002 ***
## RaceBlack -0.0278243 0.0176511 -1.576 0.115005
## RaceOther -0.0570026 0.0173079 -3.293 0.000996 ***
## SomeCollege 0.1504187 0.0207341 7.255 0.0000000000004622 ***
## Associate 0.1546164 0.0205437 7.526 0.0000000000000612 ***
## Bachelor 0.4212902 0.0175104 24.059 < 0.0000000000000002 ***
## Master 0.5746011 0.0242433 23.701 < 0.0000000000000002 ***
## Professional 0.8184414 0.0440417 18.583 < 0.0000000000000002 ***
## Doctoral 0.9593021 0.0482395 19.886 < 0.0000000000000002 ***
## AGEP 0.0092830 0.0006281 14.780 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4453 on 5181 degrees of freedom
## Multiple R-squared: 0.2556, Adjusted R-squared: 0.2539
## F-statistic: 148.3 on 12 and 5181 DF, p-value: < 0.00000000000000022## [[1]]
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- Coefficients Explanation
- Holding gender, race, education and age constant, married or widowed people makes $0.04 more than people who divorced or separated on average.
- Holding gender, race, education and age constant, married or widowed people makes $0.1 more than people who never married on average.
- Holding marriage, race, education and age constant, male makes $0.14 more than female on average.
- Holding marriage, gender, education and age constant, White makes $0.03 more than Black on average.
- Holding marriage, gender, education and age constant, White makes $0.06 more than Other race on average.
- Holding marriage, gender, race and age constant, people have high school education makes $0.15 less than people have some college education on average.
- Holding marriage, gender, race and age constant, people have high school education makes $0.15 less than people have associate education on average.
- Holding marriage, gender, race and age constant, people have high school education makes $0.42 less than people have bachelor’s degree on average.
- Holding marriage, gender, race and age constant, people have high school education makes $0.57 less than people have master’s degree on average.
- Holding marriage, gender, race and age constant, people have high school education makes $0.82 less than people have Professional education on average.
- Holding marriage, gender, race and age constant, people have high school education makes $0.96 less than people have doctor’s degree on average.
- Holding marriage, gender, race and education constant, people make $0.01 more as age increases on average between the age of 18 to 64.
First Model Updated:
\(Earning = \beta_0 + Divorced * \beta_1 + NeverMarried * \beta_2 + Female * \beta_3 + RaceBlack * \beta_4 + RaceOther * \beta_5 +\)
\(SomeCollege * \beta_6 + Associate * \beta_7 + Bachelor * \beta_8 + Master * \beta_9 + Professional * \beta_10 + Doctoral * \beta_11 + Age * \beta_12\)
##
## Call:
## lm(formula = PERNP ~ Widowed + Divorced + Separated + NeverMarried +
## Female + RaceBlack + RaceOther + SomeCollege + Associate +
## Bachelor + Master + Professional + Doctoral + AGEP, data = ss16ppr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -43683 -9228 -2919 5341 98762
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12598.97 1110.28 11.348 < 0.0000000000000002 ***
## Widowed 1104.92 1888.02 0.585 0.558422
## Divorced -1078.74 571.98 -1.886 0.059353 .
## Separated -1833.17 1489.22 -1.231 0.218393
## NeverMarried -2974.75 520.48 -5.715 0.00000001155 ***
## Female -4868.47 432.66 -11.252 < 0.0000000000000002 ***
## RaceBlack -1178.01 591.36 -1.992 0.046421 *
## RaceOther -2141.04 579.98 -3.692 0.000225 ***
## SomeCollege 4241.63 694.73 6.105 0.00000000110 ***
## Associate 4150.43 688.45 6.029 0.00000000177 ***
## Bachelor 12337.16 587.07 21.015 < 0.0000000000000002 ***
## Master 17795.40 812.61 21.899 < 0.0000000000000002 ***
## Professional 28133.37 1476.36 19.056 < 0.0000000000000002 ***
## Doctoral 35674.46 1617.08 22.061 < 0.0000000000000002 ***
## AGEP 284.94 21.12 13.488 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 14920 on 5179 degrees of freedom
## Multiple R-squared: 0.2466, Adjusted R-squared: 0.2446
## F-statistic: 121.1 on 14 and 5179 DF, p-value: < 0.00000000000000022## [[1]]
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## Call:
## lm(formula = log(PERNP) ~ Widowed + Divorced + Separated + NeverMarried +
## Female + RaceBlack + RaceOther + SomeCollege + Associate +
## Bachelor + Master + Professional + Doctoral + AGEP, data = ss16ppr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.56195 -0.30715 -0.03111 0.27690 1.69792
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.5841704 0.0331471 289.140 < 0.0000000000000002 ***
## Widowed 0.0167914 0.0563665 0.298 0.765794
## Divorced -0.0391735 0.0170763 -2.294 0.021829 *
## Separated -0.0437489 0.0444603 -0.984 0.325162
## NeverMarried -0.1033310 0.0155387 -6.650 0.0000000000323503 ***
## Female -0.1380595 0.0129169 -10.688 < 0.0000000000000002 ***
## RaceBlack -0.0278297 0.0176550 -1.576 0.115017
## RaceOther -0.0570606 0.0173151 -3.295 0.000989 ***
## SomeCollege 0.1505241 0.0207411 7.257 0.0000000000004534 ***
## Associate 0.1546604 0.0205537 7.525 0.0000000000000619 ***
## Bachelor 0.4214137 0.0175270 24.044 < 0.0000000000000002 ***
## Master 0.5748312 0.0242603 23.694 < 0.0000000000000002 ***
## Professional 0.8187333 0.0440766 18.575 < 0.0000000000000002 ***
## Doctoral 0.9597258 0.0482778 19.879 < 0.0000000000000002 ***
## AGEP 0.0092656 0.0006307 14.692 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4454 on 5179 degrees of freedom
## Multiple R-squared: 0.2556, Adjusted R-squared: 0.2536
## F-statistic: 127 on 14 and 5179 DF, p-value: < 0.00000000000000022## [[1]]
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Second Model:
\(Earning = \beta_0 + Female * \beta_1 + SomeCollege * \beta_2 + Associate * \beta_3 + Bachelor * \beta_4 +\)
\(Master * \beta_5 + Professional * \beta_6 + Doctoral * \beta_7\)
##
## Call:
## lm(formula = PERNP ~ Female + SomeCollege + Associate + Bachelor +
## Master + Professional + Doctoral, data = ss16ppr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -38674 -9557 -3538 5761 101580
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 23420.3 472.7 49.544 < 0.0000000000000002 ***
## Female -4680.9 442.5 -10.579 < 0.0000000000000002 ***
## SomeCollege 3254.4 713.8 4.559 0.0000052485 ***
## Associate 3916.5 708.4 5.529 0.0000000338 ***
## Bachelor 12148.9 603.5 20.130 < 0.0000000000000002 ***
## Master 17854.4 836.3 21.350 < 0.0000000000000002 ***
## Professional 28253.5 1521.5 18.570 < 0.0000000000000002 ***
## Doctoral 37519.8 1663.3 22.557 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15390 on 5186 degrees of freedom
## Multiple R-squared: 0.197, Adjusted R-squared: 0.1959
## F-statistic: 181.7 on 7 and 5186 DF, p-value: < 0.00000000000000022## [[1]]
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## Call:
## lm(formula = log(PERNP) ~ Female + SomeCollege + Associate +
## Bachelor + Master + Professional + Doctoral, data = ss16ppr)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.37759 -0.32163 -0.03395 0.29310 1.79864
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## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.93743 0.01420 699.976 < 0.0000000000000002 ***
## Female -0.13243 0.01329 -9.966 < 0.0000000000000002 ***
## SomeCollege 0.11836 0.02144 5.521 0.00000003524980 ***
## Associate 0.14704 0.02127 6.911 0.00000000000538 ***
## Bachelor 0.41489 0.01812 22.891 < 0.0000000000000002 ***
## Master 0.57651 0.02511 22.955 < 0.0000000000000002 ***
## Professional 0.82216 0.04569 17.993 < 0.0000000000000002 ***
## Doctoral 1.01987 0.04995 20.416 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4623 on 5186 degrees of freedom
## Multiple R-squared: 0.1972, Adjusted R-squared: 0.1961
## F-statistic: 181.9 on 7 and 5186 DF, p-value: < 0.00000000000000022## [[1]]
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- Coefficients Explanation
- Holding education constant, male makes $4656 more than female on average.
- Holding gender constant, people have high school education makes $0.15 less than people have some college education on average.
- Holding gender constant, people have high school education makes $0.15 less than people have associate education on average.
- Holding gender constant, people have high school education makes $0.42 less than people have bachelor’s degree on average.
- Holding gender constant, people have high school education makes $0.57 less than people have master’s degree on average.
- Holding gender constant, people have high school education makes $0.82 less than people have Professional education on average.
- Holding gender constant, people have high school education makes $0.96 less than people have doctor’s degree on average.